%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU902^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:42 AM UTC 2026
% Result : Theorem 1.32s 1.15s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 105 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 349 ( 47 ~; 18 |; 43 &; 209 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 3 con; 0-2 aty)
% ( 0 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 44 ^; 42 !; 6 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
d: $i > $o ).
thf(func_def_11,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_13,type,
sK2: $i > $o ).
thf(func_def_14,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK4: $i > $i > $o ).
thf(f50,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
$false = $true,
inference(duplicate_literal_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f42,f20]) ).
thf(f20,plain,
( ( sK2 @ ( sK0 @ sK2 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ~ ( sK2 @ ( sK0 @ sK2 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ~ ( sK2 @ ( sK0 @ sK2 ) )
& ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK2 )
= $true ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f11,f13,f13]) ).
thf(f13,plain,
( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ( ( d @ ( sK0 @ d ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: ( $i > $o ) > $i] :
( ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ( ( d @ ( X0 @ d ) )
= $true ) )
=> ( ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
& ! [X2: $i > $o,X1: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ( ( d @ ( sK0 @ d ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( $i > $o ) > $i] :
( ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ( ( d @ ( X0 @ d ) )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i] :
( ( ( d @ ( X0 @ d ) )
= $true )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) )
=> ( ( d @ ( X0 @ d ) )
!= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ( d
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) )
=> ( ( d @ ( X0 @ d ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ( ( ^ [X3: $i] :
? [X4: $i > $o] :
( ( ( X0 @ X4 )
= X3 )
& ~ ( X4 @ ( X0 @ X4 ) ) ) )
= d ) )
=> ~ ( d @ ( X0 @ d ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ( ( ^ [X3: $i] :
? [X4: $i > $o] :
( ( ( X0 @ X4 )
= X3 )
& ~ ( X4 @ ( X0 @ X4 ) ) ) )
= d ) )
=> ~ ( d @ ( X0 @ d ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
( ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
& ( ( ^ [X3: $i] :
? [X4: $i > $o] :
( ( ( X0 @ X4 )
= X3 )
& ~ ( X4 @ ( X0 @ X4 ) ) ) )
= d ) )
=> ~ ( d @ ( X0 @ d ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rGuHXuUAMD/DTF2THF_29113.p',cTHM143_pme) ).
thf(f11,plain,
( ( d @ ( sK0 @ d ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f42,plain,
! [X0: $i > $o] :
( ( $true
= ( sK2 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( ( X2 @ ( sK0 @ X2 ) )
= $true )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK0 @ X2 ) )
= $true )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK0 @ X2 ) ) )
= $false )
| ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK0 @ X2 ) )
& ( ( sK0 @ X2 )
= X1 ) )
= $false )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) ) ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( sK2 @ X1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK2 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= sK2 ),
inference(equality_resolution,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i > $o] :
( ( ( sK0 @ sK2 )
!= ( sK0 @ X0 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f12,f21]) ).
thf(f21,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= ( sK0 @ sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f12,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU902^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:36:03 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEU902^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : TPS problem THM143
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English : A lemma for the Injective Cantor Theorem X5309.
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bro09]
% 0.15/0.42 % Names : tps_0506 [Bro09]
% 0.15/0.42 % : THM143 [TPS]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0
% 0.15/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.15/0.42 % Number of atoms : 7 ( 4 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 5 ( 7 avg)
% 0.15/0.42 % Number of connectives : 13 ( 2 ~; 0 |; 2 &; 7 @)
% 0.15/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 7 ( 7 avg)
% 0.15/0.42 % Number of types : 2 ( 0 usr)
% 0.15/0.42 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.15/0.42 % Number of variables : 5 ( 1 ^; 3 !; 1 ?; 5 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.42 % : Polymorphic definitions expanded.
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(d,type,
% 0.15/0.42 d: $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(cTHM143_pme,conjecture,
% 0.15/0.42 ! [Xh: ( $i > $o ) > $i] :
% 0.15/0.42 ( ( ! [Xp: $i > $o,Xq: $i > $o] :
% 0.15/0.42 ( ( ( Xh @ Xp )
% 0.15/0.42 = ( Xh @ Xq ) )
% 0.15/0.42 => ( Xp = Xq ) )
% 0.15/0.42 & ( d
% 0.15/0.42 = ( ^ [Xz: $i] :
% 0.15/0.42 ? [Xt: $i > $o] :
% 0.15/0.42 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.15/0.42 & ( Xz
% 0.15/0.42 = ( Xh @ Xt ) ) ) ) ) )
% 0.15/0.42 => ~ ( d @ ( Xh @ d ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.12/1.12 ---- Embedded in THF ---
% 1.12/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.12 %%% Generated on Tue Feb 24 12:36:03 EST 2026
% 1.12/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.12 %%% Logic specification used:
% 1.12/1.12 %%% thf(spec, logic, $$dhol).
% 1.12/1.12
% 1.12/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rGuHXuUAMD/DTF2DTF29113.p
% See solution above
% 1.12/1.12 ------------------------
% 1.32/1.13 ---- Cleaned THF ---
% 1.32/1.13 thf(d,type,
% 1.32/1.13 d: $i > $o ).
% 1.32/1.13
% 1.32/1.13 thf(cTHM143_pme,conjecture,
% 1.32/1.13 ! [Xh: ( $i > $o ) > $i] :
% 1.32/1.13 ( ( ! [Xp: $i > $o,Xq: $i > $o] :
% 1.32/1.13 ( ( ( Xh @ Xp )
% 1.32/1.13 = ( Xh @ Xq ) )
% 1.32/1.13 => ( Xp = Xq ) )
% 1.32/1.13 & ( d
% 1.32/1.13 = ( ^ [Xz: $i] :
% 1.32/1.13 ? [Xt: $i > $o] :
% 1.32/1.13 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.32/1.13 & ( Xz
% 1.32/1.13 = ( Xh @ Xt ) ) ) ) ) )
% 1.32/1.13 => ~ ( d @ ( Xh @ d ) ) ) ).
% 1.32/1.13 ------------------------
% 1.32/1.14 % (29211)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/183Mi)
% 1.32/1.15 % (29214)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/2Mi)
% 1.32/1.15 % (29213)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/27Mi)
% 1.32/1.15 % (29215)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/2Mi)
% 1.32/1.15 % (29216)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/275Mi)
% 1.32/1.15 % (29217)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/18Mi)
% 1.32/1.15 % (29212)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29113 for (2999ds/4Mi)
% 1.32/1.15 % (29214)Instruction limit reached!
% 1.32/1.15 % (29214)------------------------------
% 1.32/1.15 % (29214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (29214)Termination reason: Unknown
% 1.32/1.15 % (29214)Termination phase: Property scanning
% 1.32/1.15 % (29215)Instruction limit reached!
% 1.32/1.15 % (29215)------------------------------
% 1.32/1.15 % (29215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (29215)Termination reason: Unknown
% 1.32/1.15 % (29215)Termination phase: Property scanning
% 1.32/1.15
% 1.32/1.15 % (29215)Memory used [KB]: 895
% 1.32/1.15 % (29215)Time elapsed: 0.002 s
% 1.32/1.15 % (29215)Instructions burned: 2 (million)
% 1.32/1.15 % (29215)------------------------------
% 1.32/1.15 % (29215)------------------------------
% 1.32/1.15
% 1.32/1.15 % (29214)Memory used [KB]: 895
% 1.32/1.15 % (29214)Time elapsed: 0.002 s
% 1.32/1.15 % (29214)Instructions burned: 2 (million)
% 1.32/1.15 % (29214)------------------------------
% 1.32/1.15 % (29214)------------------------------
% 1.32/1.15 % (29212)Instruction limit reached!
% 1.32/1.15 % (29212)------------------------------
% 1.32/1.15 % (29212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (29212)Termination reason: Unknown
% 1.32/1.15 % (29212)Termination phase: Saturation
% 1.32/1.15
% 1.32/1.15 % (29212)Memory used [KB]: 5500
% 1.32/1.15 % (29212)Time elapsed: 0.004 s
% 1.32/1.15 % (29212)Instructions burned: 5 (million)
% 1.32/1.15 % (29212)------------------------------
% 1.32/1.15 % (29212)------------------------------
% 1.32/1.15 % (29217)First to succeed.
% 1.32/1.15 % (29213)Also succeeded, but the first one will report.
% 1.32/1.15 % (29216)Also succeeded, but the first one will report.
% 1.32/1.15 % (29217)Refutation found. Thanks to Tanya!
% 1.32/1.15 % SZS status Theorem for DTF2THF_29113
% 1.32/1.15 % SZS output start Proof for DTF2THF_29113
% 1.32/1.15 thf(func_def_0, type, d: $i > $o).
% 1.32/1.15 thf(func_def_11, type, sK0: ($i > $o) > $i).
% 1.32/1.15 thf(func_def_13, type, sK2: $i > $o).
% 1.32/1.15 thf(func_def_14, type, ph3: !>[X0: $tType]:(X0)).
% 1.32/1.15 thf(func_def_15, type, sK4: $i > $i > $o).
% 1.32/1.15 thf(f50,plain,(
% 1.32/1.15 $false),
% 1.32/1.15 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.32/1.15 thf(f49,plain,(
% 1.32/1.15 ($false = $true)),
% 1.32/1.15 inference(duplicate_literal_removal,[status(thm)],[f43])).
% 1.32/1.15 thf(f43,plain,(
% 1.32/1.15 ($false = $true) | ($false = $true)),
% 1.32/1.15 inference(superposition,[status(thm)],[f42,f20])).
% 1.32/1.15 thf(f20,plain,(
% 1.32/1.15 ((sK2 @ (sK0 @ sK2)) = $false)),
% 1.32/1.15 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.32/1.15 thf(f19,plain,(
% 1.32/1.15 ((~ (sK2 @ (sK0 @ sK2))) = $true)),
% 1.32/1.15 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.32/1.15 thf(f17,plain,(
% 1.32/1.15 (((~ (sK2 @ (sK0 @ sK2))) & ((sK0 @ sK2) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))) = $true)),
% 1.32/1.15 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.32/1.15 thf(f16,plain,(
% 1.32/1.15 (((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1))))))))) @ sK2) = $true)),
% 1.32/1.15 inference(sigma_clausification,[status(thm)],[f15])).
% 1.32/1.15 thf(f15,plain,(
% 1.32/1.15 ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1)))))))))) = $true)),
% 1.32/1.15 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.32/1.15 thf(f14,plain,(
% 1.32/1.15 ($true = ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 1.32/1.15 inference(definition_unfolding,[status(thm)],[f11,f13,f13])).
% 1.32/1.15 thf(f13,plain,(
% 1.32/1.15 (d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))),
% 1.32/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.15 thf(f10,plain,(
% 1.32/1.15 (d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))) & ! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & ((d @ (sK0 @ d)) = $true)),
% 1.32/1.15 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.32/1.15 thf(f9,plain,(
% 1.32/1.15 ? [X0 : ($i > $o) > $i] : ((d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) & ! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ((d @ (X0 @ d)) = $true)) => ((d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))) & ! [X2 : $i > $o,X1 : $i > $o] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & ((d @ (sK0 @ d)) = $true))),
% 1.32/1.15 introduced(definition,[],[choice_axiom])).
% 1.32/1.15 thf(f8,plain,(
% 1.32/1.15 ? [X0 : ($i > $o) > $i] : ((d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0)))))) & ! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ((d @ (X0 @ d)) = $true))),
% 1.32/1.15 inference(flattening,[status(thm)],[f7])).
% 1.32/1.15 thf(f7,plain,(
% 1.32/1.15 ? [X0 : ($i > $o) > $i] : (((d @ (X0 @ d)) = $true) & (! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & (d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))))),
% 1.32/1.15 inference(ennf_transformation,[status(thm)],[f6])).
% 1.32/1.15 thf(f6,plain,(
% 1.32/1.15 ~! [X0 : ($i > $o) > $i] : ((! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & (d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) => ((d @ (X0 @ d)) != $true))),
% 1.32/1.15 inference(flattening,[status(thm)],[f5])).
% 1.32/1.15 thf(f5,plain,(
% 1.32/1.15 ~! [X0 : ($i > $o) > $i] : ((! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & (d = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (X0 @ Y1))) & ((X0 @ Y1) = Y0))))))) => ~((d @ (X0 @ d)) = $true))),
% 1.32/1.15 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.15 thf(f4,plain,(
% 1.32/1.15 ~! [X0 : ($i > $o) > $i] : ((! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ((^[X3 : $i] : (? [X4 : $i > $o] : (((X0 @ X4) = X3) & ~(X4 @ (X0 @ X4))))) = d)) => ~(d @ (X0 @ d)))),
% 1.32/1.15 inference(rectify,[status(thm)],[f2])).
% 1.32/1.15 thf(f2,negated_conjecture,(
% 1.32/1.15 ~! [X0 : ($i > $o) > $i] : ((! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ((^[X3 : $i] : (? [X4 : $i > $o] : (((X0 @ X4) = X3) & ~(X4 @ (X0 @ X4))))) = d)) => ~(d @ (X0 @ d)))),
% 1.32/1.15 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.15 thf(f1,conjecture,(
% 1.32/1.15 ! [X0 : ($i > $o) > $i] : ((! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) & ((^[X3 : $i] : (? [X4 : $i > $o] : (((X0 @ X4) = X3) & ~(X4 @ (X0 @ X4))))) = d)) => ~(d @ (X0 @ d)))),
% 1.32/1.15 file('/export/starexec/sandbox/tmp/tmp.rGuHXuUAMD/DTF2THF_29113.p',cTHM143_pme)).
% 1.32/1.15 thf(f11,plain,(
% 1.32/1.15 ((d @ (sK0 @ d)) = $true)),
% 1.32/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.15 thf(f42,plain,(
% 1.32/1.15 ( ! [X0 : $i > $o] : (($true = (sK2 @ (sK0 @ X0))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.32/1.15 inference(equality_resolution,[status(thm)],[f41])).
% 1.32/1.15 thf(f41,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X2) != X1) | ((X2 @ (sK0 @ X2)) = $true) | ($true = (sK2 @ X1))) )),
% 1.32/1.15 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.32/1.15 thf(f40,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ (sK0 @ X2)) = $true) | ($false = ((sK0 @ X2) = X1)) | ($true = (sK2 @ X1))) )),
% 1.32/1.15 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.32/1.15 thf(f39,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i] : (((~ (X2 @ (sK0 @ X2))) = $false) | ($true = (sK2 @ X1)) | ($false = ((sK0 @ X2) = X1))) )),
% 1.32/1.15 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.32/1.15 thf(f38,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i] : ((((~ (X2 @ (sK0 @ X2))) & ((sK0 @ X2) = X1)) = $false) | ($true = (sK2 @ X1))) )),
% 1.32/1.15 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.32/1.15 thf(f37,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK2 @ X1)) | ($false = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1))) @ X2))) )),
% 1.32/1.15 inference(pi_clausification,[status(thm)],[f29])).
% 1.32/1.15 thf(f29,plain,(
% 1.32/1.15 ( ! [X1 : $i] : (($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1))))) | ($true = (sK2 @ X1))) )),
% 1.32/1.15 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.32/1.15 thf(f28,plain,(
% 1.32/1.15 ( ! [X1 : $i] : (((sK2 @ X1) = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1)))))) )),
% 1.32/1.15 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.32/1.15 thf(f27,plain,(
% 1.32/1.15 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ X1) = (sK2 @ X1))) )),
% 1.32/1.15 inference(argument_congruence,[status(thm)],[f26])).
% 1.32/1.15 thf(f26,plain,(
% 1.32/1.15 ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) = sK2)),
% 1.32/1.15 inference(equality_resolution,[status(thm)],[f23])).
% 1.32/1.15 thf(f23,plain,(
% 1.32/1.15 ( ! [X0 : $i > $o] : (((sK0 @ sK2) != (sK0 @ X0)) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) = X0)) )),
% 1.32/1.15 inference(superposition,[status(thm)],[f12,f21])).
% 1.32/1.15 thf(f21,plain,(
% 1.32/1.15 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))) = (sK0 @ sK2))),
% 1.32/1.15 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.32/1.15 thf(f18,plain,(
% 1.32/1.15 ($true = ((sK0 @ sK2) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 1.32/1.15 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.32/1.15 thf(f12,plain,(
% 1.32/1.15 ( ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2)) )),
% 1.32/1.15 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.15 % SZS output end Proof for DTF2THF_29113
% 1.32/1.15 % (29217)------------------------------
% 1.32/1.15 % (29217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (29217)Termination reason: Refutation
% 1.32/1.15
% 1.32/1.15 % (29217)Memory used [KB]: 5500
% 1.32/1.15 % (29217)Time elapsed: 0.006 s
% 1.32/1.15 % (29217)Instructions burned: 6 (million)
% 1.32/1.15 % (29217)------------------------------
% 1.32/1.15 % (29217)------------------------------
% 1.32/1.15 % (29210)Success in time 0.014 s
%------------------------------------------------------------------------------